Analytical and numerical study of hardcore bosons in two dimensions

We study various properties of bosons in two dimensions interacting only via on-site hardcore repulsion. In particular, we use the lattice spin-wave approximation to calculate the ground-state energy, the density, the condensate density, and the superfluid density in terms of the chemical potential. We also calculate the excitation spectrum, omega(k). In addition, we perform high precision numerical simulations using the stochastic series expansion algorithm. We find that the spin-wave results describe extremely well the numerical results over the whole density range 0less than or equal torholess than or equal to1. We also compare the lattice spin-wave results with continuum results obtained by summing the ladder diagrams at low density. We find that for rholess than or equal to0.1 there is good agreement, and that the difference between the two methods vanishes as rho(2) for rho-->0. This offers the possibility of obtaining precise continuum results by taking the continuum limit of the spin-wave results for all densities. Finally, we study the finite-temperature phase transition numerically for the entire density range, and compare with low density predictions.